Fuzzy Cognitive Map Reconstruction: Dynamics Versus History

Authors

Wladyslaw Homenda, Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland\\Faculty of Economics and Informatics in Vilnius, University of Bialystok, Kalvariju G. 135, LT-08221 Vilnius, LithuaniaFollow
Agnieszka Jastrzebska, Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, PolandFollow
Witold Pedrycz, Department of Electrical & Computer Engineering, University of Alberta, Edmonton T6R 2G7 AB Canada\\ Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University Jeddah, 21589, Saudi Arabia\\ Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, PolandFollow

Author Country (or Countries)

Lithuania

Abstract

This study is concerned with a fundamental issue of time series representation for modeling and prediction with Fuzzy Cognitive Maps. We introduce two distinct time series representation schemes for Fuzzy Cognitive Map design. The first method is based on the temporal relationships, namely time series amplitude, amplitude change, and change of amplitude change (dynamics perspective). The second scheme is based on three consecutive historical observations: present value, past value and before past value (history perspective, 2nd order relationships). Introduced procedures are experimentally verified and compared on several synthetic and real-world time series of various characteristics. The history-oriented time series representation turned out to be more advantageous. Quality of FCM-based time series models and one-step-ahead predictions were measured in terms of Mean Squared Error. We have shown that models designed with history-oriented time series representation generally require less FCM nodes to be of comparable quality to models built on dynamics-oriented time series representation. As a result, with the history-oriented time series representation scheme we are able to construct simpler and better models.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100109

Recommended Citation

Homenda, Wladyslaw; Jastrzebska, Agnieszka; and Pedrycz, Witold (2016) "Fuzzy Cognitive Map Reconstruction: Dynamics Versus History," Applied Mathematics & Information Sciences: Vol. 10: Iss. 1, Article 9.
DOI: http://dx.doi.org/10.18576/amis/100109
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss1/9